a(n) = Sum_{k=0..floor(n/2)} binomial(k+1,2*n-4*k+1).

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =3a(5) =1a(6) =4a(7) =4a(8) =5a(9) =10a(10) =7a(11) =20a(12) =13a(13) =35a(14) =29a(15) =57a(16) =65a(17) =92a(18) =136a(19) =156a(20) =264a(21) =285a(22) =484a(23) =550a(24) =860a(25) =1079a(26) =1521a(27) =2092a(28) =2732a(29) =3965